Higher-order optical vortices are inherently unstable in the sense that they tend to split up in a series of vortices with unity charge. We demonstrate this vortex-splitting phenomenon in beams produced with holograms and spatial light modulators and discuss its generic and practically unavoidable nature. To analyze the splitting phenomena in detail, we use a multi-pinhole interferometer to map the combined amplitude and phase profile of the optical field. This technique, which is based on the analysis of the far-field interference pattern observed behind an opaque screen perforated with multiple pinholes, turns out to be very robust and can among others be used to study very 'dark' regions of electromagnetic fields. Furthermore, the vortex splitting provides an ultra-sensitive measurement method of unwanted scattering from holograms and other phase-changing optical elements.
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